Tagged Questions

A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calcalating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a ...

There are several analogies between diffraction patterns and Josephson junctions, especially between a double slit experiment and two Josephson junctions in a superconducting ring (like this):
Both ...

I ask this question, as someone has recently asked me this and I'm not sure I gave them a satisfactory/correct answer.
I explained that in QFT we describe particles (and there interactions) in terms ...

Consider the Hilbert space of a particle, whose position domain is confined to $q\in[0,1]$ (e.g. a particle in a box with unit width). Using
$$
1=\int_0 ^1 dq |q\rangle\langle q|
$$
and the position ...

I was reading about how a Fourier transform yields the wave-function expressed in terms of the momenta which constitute it, i.e. the wave-function in momentum space.
I'm not so good at calculus yet ...

Intro
We're looking at the Kronig-Penney model in class and one of the conundrums is related to the Kronig-Penney potential for a chain of $N$ atoms. I'm supposed to squeeze out some expression for ...

I was playing around with some equations and found a surprising relationship when I took the fourier transform of the momentum operator
Define $\hat P = \frac{\hbar}{i} \partial_x$, then $F(\hat P) = ...

I need to extract information about the typical distance between the black patches in an image like the one I attached here. I tried to perform 2D FFT on it (using OpenCF fdt function in Python), but ...

Can somebody explain, without using complicated mathematical formulas, what do real and imaginary parts of the sinus function represent?
And what are relations between them?
I cannot understand why ...

Since the change in velocity of an object at rest prior to time $t_{0}$ implies a change in acceleration — that is, let's postulate, $ \mathbb{P} $, the object would have remained still, so there was ...

I am running some molecular dynamics simulation with carbon nano tubes and calculating the velocity auto-correlation function (VACF). Each 10 time steps is writen in a file the VACF and in the final ...

According to my lecture notes, the inverse Fourier transform of an operator $\phi(p)$ is given by
$$\phi(x)=\int \frac {d^4p}{(2\pi)^4}\phi(p)e^{-ip\cdot x}.$$
As @WenChern pointed out below, Peskin ...

Consider the Laplace transform of an RC filter. For those who can't immediately summon it, refer equation (46) at this link: http://web.mit.edu/2.151/www/Handouts/FreqDomain.pdf for a refresher.
In ...

Regarding diffraction I am a little bit lost reading about reciprocal space and the space of $k$'s. As I understand it the Fourier relationship between a wavepacket $\Psi(\vec r,t)$ and the complex ...